Single Integer

The SingleInteger domain is intended to provide support in FriCAS for machine integer arithmetic. It is generally much faster than (bignum) Integer arithmetic but suffers from a limited range of values. Since FriCAS can be implemented on top of various dialects of Lisp, the actual representation of small integers may not correspond exactly to the host machines integer representation.

You can discover the minimum and maximum values in your implementation by using min and max.

min()$SingleInteger
  - 2147483648
                            Type: SingleInteger

max()$SingleInteger
  2147483647
                            Type: SingleInteger

To avoid confusion with Integer, which is the default type for integers, you usually need to work with declared variables.

a := 1234 :: SingleInteger
  1234
                            Type: SingleInteger

or use package calling

b := 124$SingleInteger
  124
                            Type: SingleInteger

You can add, multiply and subtract SingleInteger objects, and ask for the greatest common divisor (gcd).

gcd(a,b)
  2
                            Type: SingleInteger

The least common multiple (lcm) is also available.

lcm(a,b)
  76508
                            Type: SingleInteger

Operations mulmod, addmod, submod, and invmod are similar - they provide arithmetic modulo a given small integer. Here is 5 * 6 mod 13.

mulmod(5,6,13)$SingleInteger
  4
                            Type: SingleInteger

To reduce a small integer modulo a prime, use positiveRemainder.

positiveRemainder(37,13)$SingleInteger
  11
                            Type: SingleInteger

Operations And, Or, xor, and Not provide bit level operations on small integers.

And(3,4)$SingleInteger
  0
                            Type: SingleInteger

Use shift(int,numToShift) to shift bits, where i is shifted left if numToShift is positive, right if negative.

shift(1,4)$SingleInteger
  16
                            Type: SingleInteger

shift(31,-1)$SingleInteger
  15
                            Type: SingleInteger

Many other operations are available for small integers, including many of those provided for Integer.

See Also:

• )help Integer
• )show SingleInteger